Coordinated Lunar Time isn't just a concept — it can be calculated right now using well-established physics and astronomy. This article explains the mathematics behind the live LTC clock on moontimenow.com, from the reference epoch to the moon phase algorithm.
Эпоҳаи Справояи J2000.0
Every time system needs a starting point. For lunar time calculations, we use the J2000.0 epoch: January 1, 2000 at 12:00:00 UTC (noon). This is the standard astronomical reference epoch used by NASA, ESA, and astronomers worldwide.
J2000.0 corresponds to Julian Date 2451545.0. By measuring the number of days elapsed since this epoch, we can calculate how much the Moon's clock has drifted ahead of Earth's.
Формулаи Суръати Drift
The core calculation is straightforward. The relativistic drift rate is +56.02 microseconds per Earth day. To find the cumulative drift at any moment:
1. Calculate the number of days since J2000.0 (including fractional days) 2. Multiply by 56.02 microseconds 3. Add this offset to the current UTC time
For example, on January 1, 2025, approximately 9,131 days have elapsed since J2000.0. The cumulative drift is 9,131 × 56.02 = 511,418.62 microseconds, or about 0.511 seconds.
The drift rate itself comes from the difference in gravitational potential between Earth's surface and the Moon's surface, corrected for orbital velocity effects. NIST's 2024 framework paper describes the full derivation.
ΔT — Ислоҳоти Гардиши Замин
There's a subtlety in converting between astronomical time and civil time. Astronomers work in Terrestrial Time (TT), which ticks uniformly, while our clocks use UTC, which includes leap seconds to stay aligned with Earth's slightly irregular rotation.
The difference between TT and UTC is called ΔT (Delta T). For the current era (2015–2035), ΔT is approximately 69.36 seconds and changes very slowly — about −0.06 seconds per year. Our calculation uses a polynomial fit to International Earth Rotation Service (IERS) data:
ΔT ≈ 69.36 − 0.06 × (year − 2020)
This correction ensures that the lunar time shown on our clock is properly aligned with the UTC time displayed on your device.
Ҳисобҳои Фазаи Маҳ — Алгоритми Meeus
The moon phase calendar uses Jean Meeus' algorithm from Astronomical Algorithms (Chapter 49). This method calculates the precise times of new moons, full moons, and quarter moons using 25 periodic correction terms derived from the Moon's complex orbital mechanics.
The algorithm works by computing an approximate lunation number (k) for any given date, then applying trigonometric corrections based on the Moon's mean anomaly, the Sun's mean anomaly, the Moon's argument of latitude, and the longitude of the ascending node.
Separate correction tables are used for new moons (Table 49.a), full moons (Table 49.b), and quarter moons (Table 49.c/d with a W correction term). The result is accurate to approximately 2 minutes compared to U.S. Naval Observatory data.
Равшанӣ ва Номҳои Фазаҳо
Between the major phases, the Moon's illumination is calculated using piecewise interpolation between accurately computed quarter times. This approach accounts for the Moon's varying orbital speed (it moves faster at perigee, slower at apogee), providing more accurate illumination percentages than simple sinusoidal approximation.
Phase names are assigned based on the position within the lunation cycle: New Moon → Waxing Crescent → First Quarter → Waxing Gibbous → Full Moon → Waning Gibbous → Last Quarter → Waning Crescent. Phase boundaries are keyed to the calculated phase times rather than fixed fractional positions.